I'd say there are two options here. For a start, national board members might be expected to have some sort of safeguarding involvement, which means enhanced DBS checks. So, if your conviction is filtered, they shouldn't be publishing your name anymore and you can ask them to remove your name. At the same time, you could Google yourself to get all the URLs/web page addresses and include them in an application to Google remove those links from their search results, as your conviction has been spent for a long time. Either way, if it works, that's all you need. If neither works, you could still complain to the ICO. Hopefully, they'll see sense, but you might need to be very thorough in your ICO application, as has been mentioned elsewhere on here.

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If you are to punish a man retributively you must injure him. If you are to reform him you must improve him. And men are not improved by injuries. (George Bernard Shaw)

The best way would probably be to write to them directly and just tell them the conviction is spent.

I was previous a member of the national board for a sport in which they publish online every quarter to local clubs a list of suspended members. My conviction is spent from 14 years ago but when you google my name it appears on this file they publish of being suspended. How can I stop them from publishing this if any way?